“under”

Can one really work “under a time-constraint”? This seems odd to me. Since the person cannot literally be under this constraint. Would it make more sense to state, “...in the context of a time-constraint”? Or is is better to state in some other way?

It doesn't matter if a person can literally be under any constraint. We don't take idiomatic phrases ("raining cats and dogs," "not my cup of tea," etc.) literally. Nor should we expect prepositional phrases to make any literal sense.

"To be under a constraint" can be interpreted as idiomatic, much like "to be under stress." There's no reason for either phrase to be literal.